Plasma and Fusion Research: Regular Articles

Volume 9, 3402078 (2014)

Development of a Local Current Diagnostic using a Small
Rogowski Coil for a Spherical Tokamak Plasma in TST-2∗)
Hirokazu FURUI, Yoshihiko NAGASHIMA1) , Yuich TAKASE, Akira EJIRI, Hidetoshi KAKUDA,Masateru SONEHARA, Takuya OOSAKO, Naoto TSUJII, Junichi HIRATSUKA,
Kazuhiro IMAMURA, Takuma INADA, Keishun NAKAMURA, Ayaka NAKANISHI,
Takahiro SHINYA, Hiro TOGASHI, Shintarou TSUDA, Takuma WAKATSUKI
and Takashi YAMAGUCHIThe University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa city, Chiba 277-8561, Japan1)
Kyushu University, 6-1 Kasuga-koen, Kasuga city, Fukuoka 816-8580, Japan(Received 10 December 2013 / Accepted 8 April 2014)
A local current diagnostic using a small Rogowski coil was developed in the TST-2 spherical tokamak device(R = 0.38 m, a = 0.25 m, Bt = 0.3 T, Ip = 0.1 MA). A Rogowski coil is a cost eﬀective tool for local current
diagnostic that can detect the current signal directly. A new small Rogowski coil (outer diameter = 20 mm, innerdiameter = 12 mm, number of turns = 360) with small sensitivity to external magnetic ﬁelds, such as Bt and Bp ,was developed and successfully installed in the TST-2. The measured local current at the edge just inside the lastclosed ﬂux surface for ohmic heating was about 15 A.
c 2014 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: Rogowski coil, external magnetic eﬀect, local current diagnostic, local current density proﬁle, spherical tokamak
DOI: 10.1585/pfr.9.3402078

1. Introduction
In tokamak plasmas, the proﬁle of the local toroidal
current density is critical because it is aﬀected by the current drive method and aﬀects the equilibrium conﬁguration. Therefore, a method to measure the local current
density needs to be established. In TST-2@K, equilibrium
analysis suggested large current near the outboard boundary [1]. Thus, measuring such current directly is critical.
At present, current startup experiments using lower hybrid
waves are being performed on TST-2 [2], and the direct
measurements are needed to understand and optimize thecurrent startup. Measurements of the Motional Starc effect (MSE) are typically used to derive the radial proﬁleof current density [3]. This method is attractive for measuring current density; however, it is not suitable for small
tokamak devices because the NBI system is large and expensive. Another attractive tool is the small Rogowski
coil, which is an induction coil that can detect the time
derivative of electrical current [4]. In the SINP tokamak
device (R = 0.03 m, a = 0.007 m), local current near thecenter of the plasma was successfully measured using aRogowski coil (outer diameter = 17 mm, inner diameter= 7 mm, number of turns 275) for a discharge with Ip ∼20 kA and a duration of ∼ 1 ms [5]. The measurement in
TST-2 is, however, much more diﬃcult. In a tokamak discharge, there are toroidal (Bt ) and poloidal (Bp ) magnetic
author’s e-mail: furui@fusion.k.u-tokyo.ac.jp∗) This article is based on the presentation at the 23rd International Toki
Conference (ITC23).

ﬁelds that can be the main measurement error because thecoils have ﬁnite fabrication accuracy and lead to undesired
sensitivity to external ﬁelds. The typical current density
at the edge of the ohmic discharge in TST-2, which is ourtarget, is about 10 times smaller than that measured in theSINP tokamak and the discharge duration of TST-2 is 20times longer than that in the SINP tokamak, leading to asmall signal and time derivative. On the other hand, thevalues of the magnetic ﬁelds are almost the same. Therefore, the required signal to noise ratio (S N) is much higher
than that in the SINP tokamak. In addition to S N, the Rogowski coil should be suﬃciently small to not aﬀect themacroscopic plasma behavior. A numerical simulation wasperformed to estimate and reduce the sensitivity to externalﬁelds. With the help of the simulation results, a new small
Rogowski coil was designed and fabricated. The local current density for ohmic discharge plasma was measured using the Rogowski coil.

2. The Diagnostic Principle of the Rogowski CoilA Rogowski coil is an induction coil that can detect
the time derivative of the electrical current passing throughthe central hole. The relation between the current and output voltage of a Rogowski coil is given as follows:
V=μ0 NS dI,l dt(1)where μ0 is the magnetic permeability in vacuum, N is a3402078-1

c 2014 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 9, 3402078 (2014)

turn number, S is a cross-sectional area of the torus andl is a perimeter of the torus. The output voltage is proportional to N and S, and inversely proportional to l. An
ideal and precisely fabricated Rogowski coil has a constantturn density (N/l) and a constant cross-sectional area (S ).
When these are not constant, the coil becomes sensitive tothe external magnetic ﬁeld are generated by external currents. When the Rogowski coil has a constant turn density
and a cross-sectional area, its total magnetic ﬂux is as follows: [6]
Φ=SNl

 2πr
Bdl.

Fig. 1 A Rogowski coil in a tokamak discharge.

(2)0

In a Rogowski coil with some nonuniformities, the ﬂux
deviates from Eq. 2, and it is sensitive to external magneticﬁelds.

3. Numerical Evaluation of Finite
Sensitivity to External Magnetic
FieldsWe have fabricated and tested two types of Rogowskicoils. One has normal forward helical winding along
the torus and backward toroidal winding without crosssectional area, which is called return cable. The otherhas two layers of winding: one layer for forward helicalwinding and another for backward helical winding. Hereafter, these types are referred to as return winding and twolayer winding, respectively. We made 10 Rogowski coilsof each type and found that the two-layer winding always
performed better than the return winding. This is probably because of the diﬃculty in precisely adjusting the areaof the return coil. Thus, we used the two-layer windingin our experiment. To estimate and minimize the sensitivity of the two-layer winding to external magnetic ﬁelds, weperformed numerical simulations. The conﬁguration of theRogowski coil and external magnetic ﬁelds (Bz and By ) are
shown in Fig. 1. The direction of Bz and By are along thez-axis and y-axis, respectively, and the z and y directions
correspond to the toroidal and the poloidal directions in
the tokamak conﬁguration. The wire of the Rogowski coil
was represented by a set of points with three-dimensional
coordinates (r, θ, z), and fabrication error was simulated
by adding random errors to each coordinate of each point.
In the rectangular cross-section case, we need four points
per turn to deﬁne the wire. In uniform magnetic ﬁeld, theeﬀective projection areas (S x−y and S x−z ) agree with thesensitivity to external magnetic ﬁelds. These areas are calculated by summing up the projected area of the triangles
formed by two adjacent coordinates on the wire and a reference point. By adding random errors on the coordinates,
we can estimate the eﬀect of the fabrication error (i.e., S x−yand S x−z ). The relation between the output voltage andS x−y and S x−z are given as follows:
VBt = S x−y

∂Bt.
∂t(3)

Fig. 2 S x−y and S x−z of the two layer winding, where, Δr, Δz andrΔθ are errors in each direction.

VBp = S x−z∂Bp.
∂t(4)In the simulation, the outer diameter, inner diameter, thickness, and turn number of the Rogowski coil are set as
20 mm, 12 mm, 12 mm, and 240 turns, respectively. The
calculation was repeated 500 times with diﬀerent sets ofrandom errors, and the results are shown in Fig. 2. The error bar is the standard deviation derived from the 500 trials.
From Figs. 2 (a), (b) and (c), it is seen that the manufacturing errors in the θ direction tends to cause higher sensitivity
than those in the r and the z directions.

4. Optimum Winding of Two-Layer
Winding
In the previous section, it was found that minimizing
the errors in the θ direction eﬀectively reduces of S x−y andS x−z . Several winding cores with small dips at the corners
were made. By processing the dips on the core, we canprecisely set the correct number of dips and turns. Thedips are used to ﬁx (hook) the cable, and we tested three
dip arrangements. Their size and number of turns were thesame. The winding patterns (i.e., dip patterns) are shownin Fig. 3. The red and the blue lines represent the forward
and the backward windings, respectively. Surfaces A, B, C,3402078-2

Plasma and Fusion Research: Regular Articles

Volume 9, 3402078 (2014)and D are the same as that deﬁned in Fig. 1. In pattern 1,the dips in all surfaces are made in the same phase (i.e., atthe same θ). In pattern 2, the dips on both sides of surfaces
B and D are in the same phase and the dips on both sides ofsurfaces A and D are in the opposite phase, i.e., the dips areshifted by a half period. In pattern 3, the dips on both sidesof surfaces A and B are in the opposite phase and the dipson both sides of surfaces C and D are in the same phase.
The sensitivity to external magnetic ﬁelds was measured
using a Helmholtz coil. Table 1 lists the results of a particular day. For the test, we fabricated the winding coresand wound the Rogowski coils manually. The sensitivity toBz (S x−y ) was always ∼ 10−5 in the patterns. On the otherhand, the sensitivity of pattern 3 to By (S x−z ) was always
about 10 times smaller than in pattern 1 and 2. The cableis wound with a certain tension that ﬁxes the cable at eachdip when it is hooked on the dips. Therefore, it is useful
to have a zigzag pattern in addition to the uniform helicalstructure, which is necessary for the Rogowski coils. From
this point of view, the cable traversing surfaces A, C, andD in pattern 1 has almost no zigzag structure. On the other
hand, there are zigzag patterns in all surfaces of patterns 2and 3; moreover, it can be assumed that the S xy of pattern
2 is as small as that of pattern 3. To explain the experimental results, we also simulated patterns 2 and 3. No obvious
diﬀerences between the two simulated patterns were seen.

We were unable to explain why S xz for pattern 3 is better (i.e., smaller) than that of pattern 2; thus, we adopted
pattern 3.

5. Multi-Layer Rogowski CoilTo obtain large signal intensity, the cross sectional
area S and turn number N should increase and the coillength l should decrease. For the local current diagnostic, the Rogowski coil must be suﬃciently small. On theother hand, the size of the central hole of the Rogowski
coil should be large enough to enable local current to passthrough. Therefore, S and l must be determined considering these aspects. On the other hand, we can expect
larger signal for larger N. Therefore, the turn number must
increase to obtain suﬃcient signal intensity. To increase
N, we used twisted wire. If we use a twisted wire in thetwo-layer winding, we can make a four-layer Rogowski
coil. The twisted wire shortens the fabrication time andimproves durability. A small Rogowski coil with large turnnumber is wound by a thin cable that requires careful winding and increases the fabrication time. Using twisted wires,
we successfully fabricated an eight-layer Rogowski coil(Fig. 4). When we compare the one-layer winding (returntype) and the eight-layer winding, the fabrication times perunit turn are about 20 times shorter than the latter. The
eight-layer winding was better than the twelve-layer winding. In making the twelve-layer Rogowski coil, it was difﬁcult to count the number of turns in a dip. Furthermore,
it was rather diﬃcult to keep the winding uniformity in thetwelve-layer Rogowski coil. After winding the cable, itis necessary to adjust the position of the cable at the dip(dip width = 0.5 mm) using a small tool like a thin needle.
We performed the adjustment by monitoring the sensitivity, and we achieved a good performance as shown in thenext section. In the case of ohmic heating plasma, the dominant noises are the signals owing to Bz and By . We deﬁnethe S N ratios as S N(Bz ), S N(By ), which are the ratios ofthe current signal to the noises in the Bz and By directions
respectively. The S N ratios depends not only on S x−y andS x−z , but also on the dimensions. Using the method described in Sec. 3, we found that the S N(Bz ) increases withFig. 3 The three fabricated patterns are shown. Surfaces A, B,
C and D denote the four surfaces of the rectangular crosssection (see Fig. 1). They are the top, inner, bottom, andouter sides, respectively.
Table 1 Sensitivity of the Rogowski coils.

patternpattern 1
pattern 2pattern 3

S x−y [m2 ]1.8 × 10−5
1 × 10−5
1.8 × 10−5

S x−z [m2 ]4 × 10−5
4 × 10−5
2 × 10−6

Fig. 4 Eight-layer Rogowski coil: Outer diameter = 20 mm; inner diameter = 12 mm; thickness = 12 mm; number ofturn 360; sensitivity = 5.0 × 10−7 Vs/A; and thickness ofthe cable = 0.12 mm.

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Plasma and Fusion Research: Regular Articles

Volume 9, 3402078 (2014)

the inner radius and thickness, whereas it decreases withincreasing outer radius. S N(By ) increases with outer radius
and it is constant with increasing thickness. On the other
hand, S N(By ) is optimized by controlling the inner radius.
The outer radius and the thickness were determined fromthe viewpoints of plasma disturbance and the fabrication.

6. Experimental Results
The sensitivities to external magnetic ﬁelds were measured using a Helmholtz coil. The Rogowski coil wasplaced on the central position of the Helmholtz coil anda function generator was employed to produce sinusoidal
current. The typical frequency for the calibration was
500 Hz, which is far from the characteristic frequency(300 kHz) of the Rogowski coil. Because the output signal of the Rogowski coil was very small, an ampliﬁer
with a gain of 100 was used. The S x−y and S x−z were1.37 × 10−6 m2 and 5.20 × 10−6 m2 , respectively. We also
simulated S x−y and S x−z for the eight-layer Rogowski coillike Fig. 2. Comparing the calibration and simulation results, the fabrication accuracy of the eight-layer Rogowski
coil is smaller than ±0.1 mm. Furthermore, the sensitivityof the eight-layer Rogowski coil is about 100 times smaller
than that of the return Rogowski coil (see Sec. 5). Using
the eight-layer Rogowski coil, the ohmic heating of the discharge plasma was measured. In the experiment, the Rogowski coil was connected to an integrator circuit with cutoﬀ frequency of about 0.03 Hz and gain of about 1100 s−1 .
The Rogowski coil was located just inside the last closed
ﬂux surface (R = 551 mm) and the vertical position of theRogowski coil was also z = 0. Figure 5 (b) shows the timeevolution of the local current measured by the Rogowskicoil. The observed local current was about 15 A when theplasma current reached its maximum. On the other hand,the expected current for the parabolic current density proﬁle is 10 A. In the discharge, an abrupt current drop wasseen at 23 ms. This seems to be caused by an internal reconnection event that redistributes the current [7].
Lastly, we estimated S N(Bz ) and S N(By ) of the Rogowski coil. Using the typical values of Bz = 0.2 T, By= 40 mT and the current density 100 kA/m2 , S N(Bz ) andS N(By ) were 12 and 15 respectively. These ratios are suﬃcient to measure the local current density because we haveno other tools for direct measurements. Rogowski coils
are sensitive to electrostatic noise and the signal can be affected by the plasma ﬂoating potential (e.g., 50 V). Thus,
we performed the following test. Two copper plates, towhich sinusoidal voltage with a frequency of 2 - 50 kHz
was applied, were attached on a Rogowski coil with analuminum shield and a Teﬂon sheet. The S N ratio wasabout 20000 for the same parameters described above. Asa result, the eﬀect of electrostatic noise is negligible.

7. Summary
A new multilayer Rogowski coil was developed. Numerical simulations were performed to estimate the eﬀectof fabrication accuracy on the performance (i.e., noise) of
the measurements. Comparing the experimental and simulation results, the Rogowski coil was successfully fabricated with an accuracy of smaller than ±0.1 mm. The Rogowski coil has a large number of turns and small sensitivity to external magnetic ﬁelds. Using the Rogowski coil,
the local current in ohmic heating of plasma was measured
and the current value was about 15 A.

Acknowledgments

This work was supported by Japan Society for thepromotion of Science Grants-in-Aid for Scientiﬁc research23360409 and 21226021.

Fig. 5 The time evolution of the plasma current (a) and the local
current measured by the Rogowski coil (b).

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